Problem: Solve for $n$: $|n + 6| = 2 - n$.
Answer: Case 1: $n+6 \ge 0$ $$|n + 6| = n + 6 = 2 - n.$$Solve for $n$: $2n=-4,$ so we have $n =-2$.

Case 2: $n+6 \le 0$ $$|n + 6| = - n - 6 = 2 - n.$$Then we get $-6 = 2,$ which means that there are no solutions in this case.

Therefore, $n$ must be $\boxed{-2}.$